Question: Solve for $x$ : $ 5|x - 9| + 9 = 1|x - 9| + 7 $
Explanation: Subtract $ {1|x - 9|} $ from both sides: $ \begin{eqnarray} 5|x - 9| + 9 &=& 1|x - 9| + 7 \\ \\ { - 1|x - 9|} && { - 1|x - 9|} \\ \\ 4|x - 9| + 9 &=& 7 \end{eqnarray} $ Subtract ${9}$ from both sides: $ \begin{eqnarray} 4|x - 9| + 9 &=& 7 \\ \\ { - 9} &=& { - 9} \\ \\ 4|x - 9| &=& -2 \end{eqnarray} $ Divide both sides by ${4}$ $ \dfrac{4|x - 9|} {{4}} = \dfrac{-2} {{4}} $ Simplify: $ |x - 9| = -\dfrac{1}{2}$ The absolute value cannot be negative. Therefore, there is no solution.